U.S. patent application number 12/181396 was filed with the patent office on 2009-02-05 for expanded pharmacokinetic model for population studies in breast magnetic resonance imaging (mri).
This patent application is currently assigned to Siemens Medical Solutions USA, Inc.. Invention is credited to Gerardo Hermosillo Valadez, Vandana Mohan, Yoshihisa Shinagawa.
Application Number | 20090034814 12/181396 |
Document ID | / |
Family ID | 40084252 |
Filed Date | 2009-02-05 |
United States Patent
Application |
20090034814 |
Kind Code |
A1 |
Shinagawa; Yoshihisa ; et
al. |
February 5, 2009 |
Expanded Pharmacokinetic Model for Population Studies in Breast
Magnetic Resonance Imaging (MRI)
Abstract
A method for pharmacokinetic analysis, including: receiving
time-series medical image data of a patient introduced with a
contrast agent; identifying a reference region in the medical image
data; identifying a plurality of points of interest in the medical
image data; measuring an intensity of voxels in the reference
region; and for each point of interest, measure an intensity of
voxels therein, use the measured reference region and point of
interest intensities to obtain an expression relating the point of
interest's voxel concentration to that of the reference region,
wherein the expression is a five-parameter nonlinear model with no
reference to an arterial input function; and obtain values for each
of the five-parameters by solving the expression and use the
obtained values to determine whether the point of interest is
malignant.
Inventors: |
Shinagawa; Yoshihisa;
(Downingtown, PA) ; Mohan; Vandana; (Atlanta,
GA) ; Hermosillo Valadez; Gerardo; (West Chester,
PA) |
Correspondence
Address: |
SIEMENS CORPORATION;INTELLECTUAL PROPERTY DEPARTMENT
170 WOOD AVENUE SOUTH
ISELIN
NJ
08830
US
|
Assignee: |
Siemens Medical Solutions USA,
Inc.
Malvern
PA
|
Family ID: |
40084252 |
Appl. No.: |
12/181396 |
Filed: |
July 29, 2008 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60953568 |
Aug 2, 2007 |
|
|
|
Current U.S.
Class: |
382/131 |
Current CPC
Class: |
G01R 33/56366 20130101;
G01R 33/5601 20130101; G06T 2207/30068 20130101; G06T 7/0012
20130101 |
Class at
Publication: |
382/131 |
International
Class: |
G06K 9/00 20060101
G06K009/00 |
Claims
1. A method for pharmacokinetic analysis, comprising: receiving
time-series medical image data of a patient introduced with a
contrast agent; identifying a reference region in the medical image
data; identifying a plurality of points of interest in the medical
image data; measuring an intensity of voxels in the reference
region; and for each point of interest, measure an intensity of
voxels therein, use the measured reference region and point of
interest intensities to obtain an expression relating the point of
interest's voxel concentration to that of the reference region,
wherein the expression is a five-parameter nonlinear model with no
reference to an arterial input function; and obtain values for each
of the five-parameters by solving the expression and use the
obtained values to determine whether the point of interest is
malignant.
2. The method of claim 1, wherein the medical image data is
magnetic resonance (MR) image data.
3. The method of claim 1, wherein the medical image data includes
the patient's breast.
4. The method of claim 3, wherein the reference region is the
breast nipple.
5. The method of claim 3, wherein the point of interest is a
potential tumor in the patient's breast.
6. The method of claim 1, wherein the expression is represented by
the following equation:
c.sub.T(t)=(A.sub.1e.sup.-B.sup.1.sup.t+A.sub.2e.sup.-B.sup.2.sup.t)*c.su-
b.R(t)+A.sub.3c.sub.R(t) where c.sub.T(t) is a density of the
contrast agent at the point of interest, c.sub.R(t) is a density of
the contrast agent at the reference region, wherein each density is
approximated by a difference in voxel intensities at different
time-points, and wherein A.sub.1, B.sub.1, A.sub.2, B.sub.2,
A.sub.3 are the five-parameters.
7. The method of claim 6, wherein A.sub.1, B.sub.1, A.sub.2,
B.sub.2, A.sub.3 are represented by the following equations: A 1 =
K trans R v p R ( k ep - k ep R ) - K trans R v p ( k ep R v p R +
K trans R ) - v p R ( k ep v p + K trans ) v p R 2 ##EQU00013## B 1
= k ep R + K trans R v p R ##EQU00013.2## A 2 = ( k ep R - k ep ) K
trans v p R ( k ep R - k ep ) + K trans R ##EQU00013.3## B 2 = k ep
and A 3 = v p v p R ##EQU00013.4## wherein the point of interest is
comprised of an extravascular extracellular space (EES) and plasma,
and wherein v.sub.p is the plasma volume fraction, K.sup.trans is a
measure of flow of the contrast agent from the plasma to the EES,
and k.sub.ep is a measure of flow of the contrast agent from the
EES to the plasma.
8. The method of claim 6, wherein A.sub.1, B.sub.1, A.sub.2,
B.sub.2, A.sub.3 are obtained by performing a numerical
analysis.
9. The method of claim 1, wherein values of A.sub.1, B.sub.1,
A.sub.2, B.sub.2, A.sub.3 are included in a predetermined set of
values that indicate whether the point of interest is
malignant.
10. The method of claim 9, wherein the set of values is determined
automatically by a machine learning technique.
11. The method of claim 10, wherein the machine learning technique
is a quadratic linear analysis technique.
12. A system for pharmacokinetic analysis, comprising: a memory
device for storing a program; a processor in communication with the
memory device, the processor operative with the program to: receive
time-series medical image data of a patient introduced with a
contrast agent; identify a reference region in the medical image
data; identifying a plurality of points of interest in the medical
image data; measure an intensity of voxels in the reference region;
and for each point of interest, measure an intensity of voxels
therein, use the measured reference region and point of interest
intensities to obtain an expression relating the point of
interest's voxel concentration to that of the reference region,
wherein the expression is a five-parameter nonlinear model with no
reference to an arterial input function; and obtain values for each
of the five-parameters by solving the expression and use the
obtained values to determine whether the point of interest is
malignant.
13. The system of claim 12, wherein the medical image data is
magnetic resonance (MR) image data.
14. The system of claim 12, wherein the medical image data includes
the patient's breast.
15. The system of claim 14, wherein the reference region is the
breast nipple.
16. The system of claim 14, wherein the point of interest is a
potential tumor in the patient's breast.
17. The system of claim 12, wherein the expression is represented
by the following equation:
c.sub.T=(t)=(A.sub.1e.sup.-B.sup.1.sup.t+A.sub.2e.sup.-B.sup.2.sup.t)*c.s-
ub.R(t)+A.sub.3c.sub.R(t) where c.sub.T(t) is a density of the
contrast agent at the point of interest, c.sub.R(t) is a density of
the contrast agent at the reference region, wherein each density is
approximated by a difference in voxel intensities at different
time-points, and wherein A.sub.1, B.sub.1, A.sub.2, B.sub.2,
A.sub.3 are the five-parameters.
18. The system of claim 17, wherein A.sub.1, B.sub.1, A.sub.2,
B.sub.2, A.sub.3 are represented by the following equations: A 1 =
K trans R v p R ( k ep - k ep R ) - K trans R v p ( k ep R v p R +
K trans R ) - v p R ( k ep v p + K trans ) v p R 2 ##EQU00014## B 1
= k ep R + K trans R v p R ##EQU00014.2## A 2 = ( k ep R - k ep ) K
trans v p R ( k ep R - k ep ) + K trans R ##EQU00014.3## B 2 = k ep
and A 3 = v p v p R ##EQU00014.4## wherein the point of interest is
comprised of an extravascular extracellular space (EES) and plasma,
and wherein v.sub.p is the plasma volume fraction, K.sup.trans is a
measure of flow of the contrast agent from the plasma to the EES,
and k.sub.ep is a measure of flow of the contrast agent from the
EES to the plasma.
19. The system of claim 17, wherein A.sub.1, B.sub.1, A.sub.2,
B.sub.2, A.sub.3 are obtained by performing a numerical
analysis.
20. The system of claim 12, wherein values of A.sub.1, B.sub.1,
A.sub.2, B.sub.2, A.sub.3 are included in a predetermined set of
values that indicate whether the point of interest is
malignant.
21. The system of claim 20, wherein the set of values is determined
automatically by a machine learning technique.
22. The system of claim 21, wherein the machine learning technique
is a quadratic linear analysis technique.
23. A computer readable medium tangibly embodying a program of
instructions executable by a processor to perform method steps for
pharmacokinetic analysis, the method steps comprising: receiving
time-series medical image data of a patient introduced with a
contrast agent; identifying a reference region in the medical image
data; identifying a plurality of points of interest in the medical
image data; measuring an intensity of voxels in the reference
region; and for each point of interest, measure an intensity of
voxels therein, use the measured reference region and point of
interest intensities to obtain an expression relating the point of
interest's voxel concentration to that of the reference region,
wherein the expression is a five-parameter nonlinear model with no
reference to an arterial input function; and obtain values for each
of the five-parameters by solving the expression and use the
obtained values to determine whether the point of interest is
malignant.
24. A method for automatically determining an amount of wash-in and
wash-out of contrast agent in points of interest in breast magnetic
resonance imaging (MRI), comprising: receiving time-series MR data
of a patient's breast that has been introduced with a contrast
agent; identifying a plurality of potential cancerous regions of
interest in the breast by performing a computer-aided detection;
measuring an intensity of voxels in the breast nipple region; and
for each potential cancerous region, measure an intensity of voxels
therein, determine c.sub.T(t), which is a density of the contrast
agent at the potential cancerous region and, c.sub.R(t), which is a
density of the contrast agent at the reference region, wherein each
density is determined by approximating a difference in voxel
intensities at different time-points; and input the densities into
the following equation:
c.sub.T(t)=(A.sub.1e.sup.-B.sup.1.sup.t+A.sub.2e.sup.-B.sup.2.sup.t)*c.su-
b.R(t)+A.sub.3c.sub.R(t); solve the equation to obtain values for
A.sub.1, B.sub.1, A.sub.2, B.sub.2, A.sub.3; and obtain values for
each of A.sub.1, B.sub.1, A.sub.2, B.sub.2, A.sub.3 and use the
obtained values to determine the wash-in and wash-out of the
contrast agent in the potential cancerous region, which indicate
whether the potential cancerous region is malignant.
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This application claims the benefit of U.S. Provisional
Application No. 60/953,568, filed Aug. 2, 2007, the disclosure of
which is incorporated by reference herein in its entirety.
BACKGROUND OF THE INVENTION
[0002] 1. Technical Field
[0003] The present invention relates to pharmacokinetic (PK)
analysis.
[0004] 2. Discussion of the Related Art
[0005] The diagnosis of breast cancer from Magnetic Resonance
Imaging (MRI) data is a tough problem exacerbated by the fact that
a malignant lesion often displays intensity patterns similar to
benign tissues and other structures (such as the heart) in the
field of view. However, malignant tissues differ from benign
tissues in how Contrast Agents (CAs) flow in and leak out. These
molecules affect the observed intensity patterns because they
change the longitudinal relaxation times at the voxels in the
image. Unlike their behavior with respect to intensity itself,
malignant tissues display a characteristic pattern with regard to
how much of the CA they take up, and also with regard to the rates
of entry and wash-out of the CA. Dynamic Contrast-Enhanced (DCE)
MRI uses this property to identify regions of interest.
Pharmacokinetic (PK) analysis then aims to quantify the wash-in and
wash-out of the CA towards differentiating malignant and benign
lesions. The ideal goal of PK analysis in the context of breast MRI
is to provide a framework where the kinetics of the CA within the
tissue of interest can be quantitatively described, and compared
across data sets from one or more patients and/or MR systems.
However, current systems do not meet this requirement due to
difficulties in the normalization that the system can perform on
the input image data, which impairs the effectiveness of any
population studies conducted.
[0006] Existing literature on PK analysis for breast MR can be
categorized into two broad classes of models--compartmental and
heuristic. The first class attempts to describe the microscopic
view of the breast tissues as a set of compartments and then models
the interaction between these compartments with respect to the
entry and exit of the CA. Within this class, the models differ in
the number of compartments they use to model the tissue and the
equations that describe the interactions. Heuristic models attempt
to model the wash-in and wash-out phenomena--as growing(/decaying)
exponentials for example--and quantify the extents and rates of the
same. Of the compartmental models, the Tofts model is the most
commonly used. A comparative study of different PK models for
DCE-MRI can be found, for example, in [R. Srikanchana, D.
Thomasson, P. Choyke, and A. Dwyer. A comparison of pharmacokinetic
models of dynamic contrast-enhanced MRI. CBMS 2004. Proceedings.
17.sup.th IEEE Symposium on Computer-Based Medical Systems, 2004,
pages 361-366, 2004]. The challenges in estimating the quantity of
CA in the vascular space and the unsatisfactory normalization which
impairs population studies are key issues that need to be
addressed.
SUMMARY OF THE INVENTION
[0007] In an exemplary embodiment of the present invention, a
method for pharmacokinetic analysis, comprises: receiving
time-series medical image data of a patient introduced with a
contrast agent; identifying a reference region in the medical image
data; identifying a plurality of points of interest in the medical
image data; measuring an intensity of voxels in the reference
region; and for each point of interest, measure an intensity of
voxels therein, use the measured reference region and point of
interest intensities to obtain an expression relating the point of
interest's voxel concentration to that of the reference region,
wherein the expression is a five-parameter nonlinear model with no
reference to an arterial input function; and obtain values for each
of the five-parameters by solving the expression and use the
obtained values to determine whether or not the point of interest
is malignant.
[0008] The medical image data is magnetic resonance (MR) image
data. The medical image data includes the patient's breast. The
reference region is the breast nipple. The point of interest is a
potential tumor in the patient's breast.
[0009] The expression is represented by the following equation:
c.sub.T(t)=(A.sub.1e.sup.-B.sup.1.sup.t+A.sub.2e.sup.-B.sup.2.sup.t)*c.s-
ub.R(t)+A.sub.3c.sub.R(t)
where c.sub.T(t) is a density of the contrast agent at the point of
interest, c.sub.R(t) is a density of the contrast agent at the
reference region, wherein each density is approximated by a
difference in voxel intensities at different time-points, and
wherein A.sub.1, B.sub.1, A.sub.2, B.sub.2, A.sub.3 are the
five-parameters.
[0010] A.sub.1, B.sub.1, A.sub.2, B.sub.2, A.sub.3 are represented
by the following equations:
A 1 = K trans R v p R ( k ep - k ep R ) - K trans R v p ( k ep R v
p R + K trans R ) - v p R ( k ep v p + K trans ) v p R 2
##EQU00001## B 1 = k ep R + K trans R v p R ##EQU00001.2## A 2 = (
k ep R - k ep ) K trans v p R ( k ep R - k ep ) + K trans R
##EQU00001.3## B 2 = k ep and A 3 = v p v p R ##EQU00001.4##
wherein the point of interest is comprised of an extravascular
extracellular space (EES) and plasma, and wherein v.sub.p is the
plasma volume fraction, K.sup.trans is a measure of flow of the
contrast agent from the plasma to the EES, and k.sub.ep is a
measure of flow of the contrast agent from the EES to the
plasma.
[0011] A.sub.1, B.sub.1, A.sub.2, B.sub.2, A.sub.3 are obtained by
performing a numerical analysis.
[0012] Values of A.sub.1, B.sub.1, A.sub.2, B.sub.2, A.sub.3 are
included in a predetermined set of values that indicate whether the
point of interest is malignant. The set of values is determined
automatically by a machine learning technique. The machine learning
technique is a quadratic linear analysis technique.
[0013] In an exemplary embodiment of the present invention, a
system for pharmacokinetic analysis, comprising: a memory device
for storing a program; a processor in communication with the memory
device, the processor operative with the program to: receive
time-series medical image data of a patient introduced with a
contrast agent; identify a reference region in the medical image
data; identifying a plurality of points of interest in the medical
image data; measure an intensity of voxels in the reference region;
and for each point of interest, measure an intensity of voxels
therein, use the measured reference region and point of interest
intensities to obtain an expression relating the point of
interest's voxel concentration to that of the reference region,
wherein the expression is a five-parameter nonlinear model with no
reference to an arterial input function; and obtain values for each
of the five-parameters by solving the expression and use the
obtained values to determine whether or not the point of interest
is malignant.
[0014] The medical image data is magnetic resonance (MR) image
data. The medical image data includes the patient's breast. The
reference region is the breast nipple. The point of interest is a
potential tumor in the patient's breast.
[0015] The expression is represented by the following equation:
c.sub.T(t)=(A.sub.1e.sup.-B.sup.1.sup.t+A.sub.2e.sup.-B.sup.2.sup.t)*c.s-
ub.R(t)+A.sub.3c.sub.R(t)
where c.sub.T(t) is a density of the contrast agent at the point of
interest, c.sub.R(t) is a density of the contrast agent at the
reference region, wherein each density is approximated by a
difference in voxel intensities at different time-points, and
wherein A.sub.1, B.sub.1, A.sub.2, B.sub.2, A.sub.3 are the
five-parameters.
[0016] A.sub.1, B.sub.1, A.sub.2, B.sub.2, A.sub.3 are represented
by the following equations:
A 1 = K trans R v p R ( k ep - k ep R ) - K trans R v p ( k ep R v
p R + K trans R ) - v p R ( k ep v p + K trans ) v p R 2
##EQU00002## B 1 = k ep R + K trans R v p R ##EQU00002.2## A 2 = (
k ep R - k ep ) K trans v p R ( k ep R - k ep ) + K trans R
##EQU00002.3## B 2 = k ep and A 3 = v p v p R ##EQU00002.4##
wherein the point of interest is comprised of an extravascular
extracellular space (EES) and plasma, and wherein v.sub.p is the
plasma volume fraction, K.sup.trans is a measure of flow of the
contrast agent from the plasma to the EES, and k.sub.ep is a
measure of flow of the contrast agent from the EES to the
plasma.
[0017] A.sub.1, B.sub.1, A.sub.2, B.sub.2, A.sub.3 are obtained by
performing a numerical analysis.
[0018] Values of A.sub.1, B.sub.1, A.sub.2, B.sub.2, A.sub.3 are
included in a predetermined set of values that indicate whether the
point of interest is malignant. The set of values is determined
automatically by a machine learning technique. The machine learning
technique is a quadratic linear analysis technique.
[0019] In an exemplary embodiment of the present invention, a
computer readable medium tangibly embodying a program of
instructions executable by a processor to perform method steps for
pharmacokinetic analysis, the method steps comprising: receiving
time-series medical image data of a patient introduced with a
contrast agent; identifying a reference region in the medical image
data; identifying a plurality of points of interest in the medical
image data: measuring an intensity of voxels in the reference
region; and for each point of interest, measure an intensity of
voxels therein, use the measured reference region and point of
interest intensities to obtain an expression relating the point of
interest's voxel concentration to that of the reference region,
wherein the expression is a five-parameter nonlinear model with no
reference to an arterial input function; and obtain values for each
of the five-parameters by solving the expression and use the
obtained values to determine whether or not the point of interest
is malignant.
[0020] In an exemplary embodiment of the present invention, a
method for automatically determining an amount of wash-in and
wash-out of contrast agent in points of interest in breast magnetic
resonance imaging (MRI), comprises: receiving time-series MR data
of a patient's breast that has been introduced with a contrast
agent; identifying a plurality of potential cancerous regions of
interest in the breast by performing a computer-aided detection;
measuring an intensity of voxels in the breast nipple region; and
for each potential cancerous region, measure an intensity of voxels
therein, determine c.sub.T(t), which is a density of the contrast
agent at the potential cancerous region and, c.sub.R(t), which is a
density of the contrast agent at the reference region, wherein each
density is determined by approximating a difference in voxel
intensities at different time-points; and input the densities into
the following equation:
c.sub.T(t)=(A.sub.1e.sup.-B.sup.1.sup.t+A.sub.2e.sup.-B.sup.2.sup.t)*c.s-
ub.R(t)+A.sub.3c.sub.R(t);
solve the equation to obtain values for A.sub.1, B.sub.1, A.sub.2,
B.sub.2, A.sub.3; and obtain values for each of A.sub.1, B.sub.1,
A.sub.2, B.sub.2, A.sub.3 and use the obtained values to determine
the wash-in and wash-out of the contrast agent in the potential
cancerous region, which indicate whether or not the potential
cancerous region is malignant.
[0021] The foregoing features are of representative embodiments and
are presented to assist in understanding the invention. It should
be understood that they are not intended to be considered
limitations on the invention as defined by the claims, or
limitations on equivalents to the claims. Therefore, this summary
of features should not be considered dispositive in determining
equivalents. Additional features of the invention will become
apparent in the following description, from the drawings and from
the claims.
BRIEF DESCRIPTION OF THE DRAWINGS
[0022] FIG. 1 is a microscopic view of Tofts' two-compartment
model;
[0023] FIGS. 2A and 2B illustrate a framework for a pharmacokinetic
(PK) model in accordance with an exemplary embodiment of the
present invention;
[0024] FIGS. 3A and 3B include images illustrating results of
comparing a manually segmented ground truth with results from the
Tofts model and the PK model in accordance with an exemplary
embodiment of the present invention;
[0025] FIG. 4 illustrates Receiver Operating Characteristic (ROC)
curves for (a) the Tofts model and (b) the PK model in accordance
with an exemplary embodiment of the present invention;
[0026] FIG. 5 is a flow diagram of a method for PK analysis in
accordance with an exemplary embodiment of the present invention;
and
[0027] FIG. 6 is a block diagram of a system in which exemplary
embodiments of the present invention may be implemented.
DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS
1. Introduction
[0028] Presented herein, in accordance with an exemplary embodiment
of the present invention, is a model for pharmacokinetic (PK)
analysis based on the Tofts model. Our model both eliminates the
need for estimating the Arterial Input Function (AIF) and
normalizes analysis so that comparisons across patients can be
performed. Previous models have attempted to circumvent the AIF
estimation by using the PK parameters of multiple reference regions
(RR). Viewing anatomical structures as filters, PK analysis tells
us that `similar` structures will be similar filters. By cascading
the inverse filter at a RR with the filter at the voxel being
analyzed, we obtain a transfer function relating the concentration
of a voxel to that of the RR. We show that this transfer function
simplifies into a five-parameter nonlinear model with no reference
to the AIF. These five parameters are combinations of the three
parameters of the original model and the RR at the region of
interest. Contrary to existing methods, ours does not require
explicit estimation of the PK parameters of the RR. Also, cascading
filters in the frequency domain allows us to manipulate more
complex models, such as accounting for the vascular tracer
component. We believe that our model can improve analysis across
magnetic resonance (MR) parameters because the analyzed and
reference enhancement series are from the same image. Initial
results are promising with the model parameters exhibiting values
that are more consistent across lesions in multiple patients.
Additionally, our model can be applied to multiple voxels to
estimate the original PK parameters as well as the AIF.
2.1 Tofts Model
[0029] The model presented herein uses the Tofts two-compartment
model [P. S. Tofts, G. Brix, D. L. Buckley, J. L. Evelhoch, E.
Henderson, M. V. Knopp, H. B. W. Larsson, T. Y. Lee, N. A. Mayr, G.
J. M. Parker, et al. Estimating kinetic parameters from dynamic
contrast-enhanced T1-weighted MRI of diffusible tracer: a common
global language for standardized quantities and symbols. J. Magn.
Reson. Imaging, 10:223-232, 1999] to describe the concentration at
each voxel within the image with respect to the true AIF. By
applying the idea of a RR, it uses the expressions at two different
voxels towards analytically eliminating the AIF from the
analysis.
[0030] The Tofts model is a simplified model that considers the
tissue of interest as one compartment (Extravascular Extracellular
Space or EES) and everything extraneous to it as another
compartment (Plasma) and models the kinetics of the contrast agent
as an exchange between the two. The cells are not included in
either of these compartments because by the nature of the contrast
agents (CAs) of interest in this work, the CA (or the tracer)
cannot diffuse into the cells. The rates and the exchange between
the two compartments are denoted by the PK parameters K.sup.trans
and k.sub.ep. This is clearly illustrated in FIG. 1.
[0031] This model is chosen for its relative simplicity among
compartmental models and over heuristic models since it describes
the physical behavior of the underlying structure and is hence more
intuitive. It starts from the differential equation describing the
exchange of the CA as described in FIG. 1:
c e ( t ) t = K trans c p ( t ) - k ep c e ( t ) ( 1 )
##EQU00003##
where K.sup.trans quantifies the flow of CA from the plasma to the
EES and k.sub.ep quantifies the flow of CA from the EES to the
plasma. c.sub.p(t) is the AIF and is the term that represents the
CA concentration in the plasma surrounding the EES, which is
effectively the `input` to the EES itself.
[0032] The solution for this differential equation is:
c.sub.e(t)=K.sup.transc.sub.p(t)*e.sup.-k.sup.rp.sup.t (2)
[0033] It is important to note that this expression only accounts
for the tracer (equivalent to CA) component in the EES itself. In
certain scenarios (discussed in detail in [P. S. Tofts, G. Brix, D.
L. Buckley, J. L. Evelhoch, E. Henderson, M. V. Knopp, H. B. W.
Larsson, T. Y. Lee, N. A. Mayr, G. J. M. Parker, et al. Estimating
kinetic parameters from dynamic contrast-enhanced T1-weighted MRI
of diffusible tracer: a common global language for standardized
quantities and symbols. J. Magn. Reson. Imaging, 10:223-232,
1999]), the vascular tracer component cannot be neglected. The
extended Tofts model takes this component into account to yield the
following expression for the total concentration:
c.sub.T(t)=v.sub.pc.sub.p(t)+K.sup.transc.sub.p(t)*e.sup.-k.sup.rp.sup.t-
(3)
[0034] The first term denotes the vascular tracer and the second
denotes the tracer in the EES as a result of the exchange between
the two compartments. The AIF (c.sub.p(t)) is unique to each
patient and crucial because, as noted previously the tracer
concentration in the plasma (explained further in [T. E. Yankeelov,
J. J. Luci, M. Lepage, R. Li., L. Debusk, P. C. Lin, R. R. Price,
and J. C. Gore. Quantitative pharmacokinetic analysis of DCE-MRI
data without an arterial input function: a reference region model.
Magnetic Resonance Imaging, 23(4):519-529, 2005]) is the input to
the tissue itself.
[0035] The different approaches to handle the AIF are not discussed
in this disclosure. The interested reader is referred to [P. S.
Tofts, G. Brix, D. L. Buckley, J. L. Evelhoch, E. Henderson, M. V.
Knopp, H. B. W. Larsson, T. Y. Lee, N. A. Mayr, G. J. M. Parker, et
al. Estimating kinetic parameters from dynamic contrast-enhanced T
1-weighted MRI of diffusible tracer: a common global language for
standardized quantities and symbols. J. Magn. Reson. Imaging,
10:223-232, 1999]. We are interested in the most generic case where
analysis is to be performed in the absence of a measured AIF. In
this case, the following model is widely used as a standard AIF
(e.g., [R. Srikanchana, D. Thomasson, P. Choyke, and A. Dwyer. A
comparison of pharmacokinetic models of dynamic contrast-enhanced
MRI. CBMS 2004. Proceedings. 17.sup.th IEEE Symposium on
Computer-Based Medical Systems, 2004, pages 361-366, 2004]):
c p ( t ) = D i = 1 2 a i - m i t ( 4 ) ##EQU00004##
where D is the dosage per kg body weight, and a.sub.is and m.sub.is
are constants that describe the bi-exponential decay of the
AIF.
[0036] The three parameters to be estimated for this original model
are:
1. v.sub.p: the plasma volume. This is physically analogous to a
volume fraction. (Unit: A.U. (Arbitrary Unit)) 2. K.sup.trans:
measure of the flow of CA from the plasma to the EES. (Unit:
A.U./min) 3. k.sub.ep: measure of the flow of CA from the EES to
the plasma. (Unit: min.sup.-1)
[0037] The use of A.U. in the units for the above quantities is
because, though the model is defined on concentration, in practice,
we fit it to the observed signal intensity. This same
implementation detail also accounts for why the values do not meet
the exact conditions outlined in [P. S. Tofts, G. Brix, D. L.
Buckley, J. L. Evelhoch, E. Henderson, M. V. Knopp, H. B. W.
Larsson, T. Y. Lee, N. A. Mayr, G. J. M. Parker, et al. Estimating
kinetic parameters from dynamic contrast-enhanced T1-weighted MRI
of diffusible tracer: a common global language for standardized
quantities and symbols. J. Magn. Reson. Imaging, 10:223-232, 1999].
For example, though K.sup.trans is ideally expected to be much
smaller in value than k.sub.ep, we have generally observed the
opposite to be true. Thus, the volume fraction v.sub.e that we
actually compute will be greater than 1 (and it will be in units of
A.U. rather than dimensionless).
2.2 Role of AIF in PK Analysis
[0038] In compartmental models, PK analysis models the interaction
between the compartments or sections of the anatomical structure
under study. While these models are theoretically superior to
heuristic models in describing the underlying anatomy, the
disadvantage is that the `input` to these strictures needs to be
known apriori. It is simply the CA concentration in the blood being
fed to the first compartment in the model, and is referred to as
the AIF. As is obvious from the equations for the Tofts model, the
accuracy in estimating the AIF directly affects the accuracy of the
estimated PK parameters. The primary difficulty is, however, in
measuring this quantity reliably, and this motivates an entire
family of approaches that attempt to analytically eliminate the AIF
from PK analysis or to circumvent its estimation by other means.
The category of approaches that use data from other regions within
the image towards the AIF are typically referred to as RR
approaches. The compartmental approach and the role of the AIF can
be found in greater detail in [R. E. Port, M. V. Knopp, U. Hoffman,
S. Milker-Zabel, and G. Brix. Multicompartment analysis of
gadolinium chelate kinetics: Blood-tissue exchange in mammary
tumors as monitored by dynamic MR imaging. Journal of Magnetic
Resonance Imaging, 10(3):233-241, 1999], [N. E. Simpson, Z. He, and
J. L. Evelhoch. Deuterium NMR tissue perfusion measurements using
the tracer uptake approach: I. Optimization of methods. Magn.
Reson. Med., 42:42-52, 1999] and [H. J. Weinmann, M. Laniado, and
W. Mutzel. Pharmacokinetics of GdDTPA/dimeglumine after intravenous
injection into healthy volunteers. Physiological chemistry and
physics and medical NMR, 16(2):167-172, 1984].
2.3 RR Approaches
[0039] The basic assumption behind RR approaches to PK analysis is
that all regions within a given image have the same AIF if the
effects of differences in dispersion are neglected. The approach
then is to relate the concentration at the region being analyzed to
that of a RR, and to eliminate the AIF between the two expressions.
The framework of the present invention is derived starting from a
similar premise. However, the formulation is such that the PK
analysis can be performed in a different parameter space, with no
assumptions of the parameters for the RR, while simultaneously
ensuring that with appropriate choice of the RR, the PK parameters
are naturally normalized so that data from different patients can
be compared, making population studies feasible.
3. Our PK Model
[0040] The PK model uses the Tofts model to describe the
concentration at each voxel with respect to the true AIF for the
case, and subsequently eliminates AIF by directly relating
concentration at the voxel being analyzed to the reference voxel
concentration.
3.1 Derivation of PK Model Equation
[0041] Using Tofts model, we write the expressions for the
concentration at the analyzed and reference voxels as:
c.sub.T(t)=v.sub.pc.sub.p(t)+K.sup.transc.sub.p(t)*e.sup.-k.sup.rp.sup.t
(5)
c.sub.R(t)=v.sub.p.sup.Rc.sub.p(t)+K.sup.trans.sup.Rc.sub.p(t)*e.sup.-k.-
sup.rp.sup.k.sup.t (6)
[0042] Here, c.sub.T(t) denotes the concentration at the voxel
being analyzed, c.sub.R(t) denotes the concentration at the
reference voxel, c.sub.pt) denotes the true AIF, v.sub.p,
K.sup.trans and k.sub.ep are the Tofts model parameters for the
voxel being analyzed, v.sub.p.sup.R, K.sup.trans.sup.R and
k.sub.ep.sup.R are the Tofts model parameters for the reference
voxel.
[0043] Applying the Laplace transform to equations (5) and (6), we
obtain
C T ( s ) = v p C p ( s ) + K trans C p ( s ) 1 s + k ep ( 7 )
##EQU00005##
and
C R ( s ) = v p R C p ( s ) + K trans R C p ( s ) 1 s + k ep R ( 8
) ##EQU00006##
where C.sub.T(s), C.sub.R(s) and C.sub.p(s) are the Laplace
transforms of c.sub.T(t), C.sub.R(t) and c.sub.p(t)
respectively.
[0044] Dividing equation (7) by (8) and simplifying using partial
fractions, we get
C T ( s ) C R ( s ) = A 1 s + B 1 + A 2 s + B 2 + A 3 ( 9 )
##EQU00007##
where
A 1 = K trans R v p R ( k ep - k ep R ) - K trans R v p ( k ep R v
p R + K trans R ) - v p R ( k ep v p + K trans ) v p R 2 B 1 = k ep
R + K trans R v p R A 2 = ( k ep R - k ep ) K trans v p R ( k ep R
- k ep ) + K trans R B 2 = k ep and A 3 = v p v p R ( 10 )
##EQU00008##
[0045] Taking the inverse Laplace transform, we obtain the
expression for the current voxel's concentration time series in
terms of that of the reference voxel as
c.sub.T(t)=(A.sub.1e.sup.-B.sup.1.sup.t+A.sub.2e.sup.-B.sup.2.sup.t)*c.s-
ub.R(t)+A.sub.3c.sub.R(t) (11)
[0046] For the sake of completeness, we also need to consider the
case of when the transfer function has repeated poles. This is the
case when the following condition holds.
k ep R + K trans R v p R = k ep ( 12 ) ##EQU00009##
[0047] In this special case, by a similar approach using the
Laplace transform and the partial fractions simplification, we
obtain the following transfer function:
C T ( s ) C R ( s ) = C 1 s ( s + B ) 2 + C 2 ( s + B ) + C 3 ( 13
) ##EQU00010##
where
C 1 = - K trans ( k ep R - k ep ) v p R k ep , C 2 = v p v p R k ep
[ { k ep + K trans v p } k ep R - k ep 2 ] C 3 = v p v p R B = k ep
R + K trans R v p R = k ep ( 14 ) ##EQU00011##
[0048] Taking the inverse Laplace transform, we obtain the
following expression relating the current voxel's concentration to
that of the RR:
c.sub.T(t)=C.sub.1(Bt+1)e.sup.-Bt*C.sub.R(t)+C.sub.2e.sup.-Bt*C.sub.R(t)-
+C.sub.3C.sub.R(t) (11)
3.2 Justification for the PK Model
[0049] Viewing anatomical structures as filters, we can denote the
responses for the reference and analysis regions in different
images. Let us consider two images I.sub.1 and I.sub.2 (i.e., from
different patients). Let H.sub.1 denote the filter response of the
RR in I.sub.1, and Q.sub.1 denote the filter response of the
analyzed region in I.sub.1. Similarly, let H.sub.2 and Q.sub.2
denote the filter responses of the RR and analysis region
respectively, in I.sub.2.
[0050] To correlate with the original PK coefficients, Q.sub.i is
analogous to v.sub.p.sup.i, K.sup.trans.sup.t and k.sub.ep.sup.i,
where the latter are the PK coefficients for the analyzed voxel in
I.sub.i when i=1, 2 etc. PK analysis compares Q.sub.1 and Q.sub.2.
Our approach amounts to comparing H.sub.1.sup.-1Q.sub.1 and
H.sub.2.sup.-1Q.sub.2. Since the RRs are assumed to be the same
structure from different images, H.sub.1=H.sub.2. Thus, the two
frameworks yield the same effective comparison. (See FIG. 2 for the
anatomical and filter views).
3.3 Uniqueness of Our Approach
[0051] The work in [T. E. Yankeelov, J. J. Luci, M. Lepage, R. Li.,
L. Debusk, P. C. Lin, R. R. Price, and J. C. Gore. Quantitative
pharmacokinetic analysis of DCE-MRI data without an arterial input
function: a reference region model. Magnetic Resonance Imaging,
23(4):519-529, 2005] clearly explains the significance of the AIF
and the goal of RR approaches with regards to AIF elimination. Our
framework differs from existing RR approaches (e.g., [T. E.
Yankeelov, J. J. Luci, M. Lepage, R. Li., L. Debusk, P. C. Lin, R.
R. Price, and J. C. Gore. Quantitative pharmacokinetic analysis of
DCE-MRI data without an arterial input function: a reference region
model. Magnetic Resonance Imaging, 23(4):519-529, 2005]) in certain
key aspects. For example, it is based on the extended model
accounting for the vascular CA component and is thus more generic.
Also, we do not need to assign the values of the PK parameters of
the RR. Additionally, the structure of our model is such that no
additional measurements or calibration are needed in MR
acquisition.
3.4 Potential Sources of Error in Our Model
[0052] It is important to note that our model--like all PK
models--describes the time-evolution of CA concentration. However,
in DCE-MRI, the concentration is not directly accessible and
instead, observed signal intensities are related to it nonlinearly.
The linear approximation employed in the process of fitting the
signal intensities to the derived relationships, could be a
potential source of error for our framework. In theory, we could
account for the analytic relationship between intensity and CA
concentration and write the model directly in terms of intensities.
However, this would lead to a more complicated model and hence
increase computation requirements. Hence, the extent of this effect
is first being studies through experiments. Also, the extent of
normalization achieved is sensitive to how consistently the RR can
be chosen over images.
4. Implementation and Experiments
[0053] In this work, the conjugate-gradient technique was chosen to
estimate the parameters of our model. Also, in looking at the
expressions for the parameters, we observe that B.sub.1 is only
dependent upon the original (Tofts model) PK parameters of the RR.
This implies that by definition, this quantity is expected to be
the same for all the voxels in the given image. Thus, in our
implementation, we constrain B.sub.1 to be the same across all
voxels of an image as well as across images. An automatic module
for the nipple detection in [Mert Dikmen, Yiqiang Zhan, and Xing
Sean Zhou. Joint Detection and Localization of Multiple Anatomical
Landmarks through Learning. SPIE Medical Imaging, 2008] was used.
The technique was tested over a population comprising 40 data sets,
each from a different patient. Candidate lesions within each data
set were made available through a semi-automatic segmentation of
the 20 largest lesions in each data set, and this was used to
evaluate the performance of our framework by comparison to the
ground truth. Also, the parameter distribution within lesions for
all these cases was studied to identify patterns that could be used
to distinguish malignant and benign lesions.
[0054] Note that the special case of the repeated poles in Equation
15 is mentioned in this disclosure for completeness. In practice,
it is not possible to know apriori which model should be fit to the
data being analyzed since that would require knowledge of the
parameters of the Tofts model itself. A simple solution would be to
attempt to fit both models to each voxel and pick the one with a
lower value of error. However, due to the increased computational
burden that this would present, we chose to fit the general model
as given in Equation 9 everywhere.
5. Results
[0055] FIG. 3 shows the results of the experiments comparing PK
analysis using Tofts model with our model. All five cases included
here were malignant. Column 1 indicates the ground truth, while
Columns 2 and 3 show the regions of interest as localized by
analysis using the Tofts model and our model, respectively. The
data in these figures (on which the localized regions of interest
are superimposed in color with blue being the highest value--note
blue color is indicated by regions with clearly delineated borders)
is inverted so that in interpreting these figures, darker regions
indicate greater enhancement and brighter regions indicate lesser
enhancement. The lesion localization and lesion areas as indicated
in these images can be directly compared to compare the performance
of the two models.
5.1 Observations
[0056] The estimated parameters for our five-parameter model are
observed to be better correlated across different patients than the
original Tofts parameters as estimated with the standard AIF.
However, the parameters are sensitive to the RR chosen and hence
the extent of normalization across patients is dependent on how
consistently the RR is chosen across images. The current RR of
choice is the nipple region. The main reasons for this choice are
that the enhancement characteristics of the nipple are relatively
similar across images and also that the nipple is a relatively
clear structure and easy to automatically locate in the breast MR.
An alternate choice for the RR would be the pectoral muscle. It is
also important to note that there are breast MR images in which the
nipple is not clear or not seen or in cases of lumpectomy, the
nipple might be missing in which case a structure like the pectoral
muscle might prove more reliable as a RR.
[0057] As is clear in FIG. 3, visually our model localizes the
malignant lesions better than the analysis that uses the Tofts
model with a standard AIF. Also, the number of false positives or
spurious voxels picked up is far lesser for our model. These two
aspects clearly demonstrate the effectiveness of our model in
visually highlighting suspicious voxels for further analysis by
radiologists. In order to better understand the performance of our
model in population studies, both the framework of our model and
the framework based on the Tofts model were applied to all 40 data
sets. The results from classification using both approaches were
compared using Receiver Operating Characteristics (ROC) curves.
There are shown in FIG. 4. These clearly indicate that our model
allows better classification than the extended Tofts model, in the
sense of yielding higher sensitivity than the latter at comparable
discrimination thresholds. This clearly illustrates the potential
for out model in population studies. It is also expected that with
more robust RR selection and more accurate model fitting, the
classification accuracy obtained with our model can be improved
further.
6. Conclusions and Future Work
[0058] The work discussed in this disclosure describes a model for
PK analysis based on the Tofts model. The new model offers the
advantages of eliminating the estimation of the AIF, and
normalizing the resulting parameters so as to facilitate population
studies. In our experiments across 40 patients, the estimated
parameters for our model displayed greater correlation across
patients than did the Tofts model parameters (with standard AIF).
Also, on visual inspection and by thresholding, the results from
our model were less noisy while still capturing most of the lesion
area which is very promising.
[0059] Since our model parameters are functions of those of the
Tofts model at the voxels being analyzed and used for reference, it
is theoretically possible to estimate the Tofts model parameters
without the AIF estimation or to directly estimate the AIF for any
subsequent analysis by using our framework. Using this framework on
a pair of voxels yields five parameters that are functions of the
original PK parameters (three each) of the two individual voxels.
Using v voxels, there would be 3v unknowns and
5 v ( v - 1 ) 2 ##EQU00012##
equations. Solving the inequality, we see that three or more voxels
will be sufficient for solving for the individual PK parameter
values. We can then use the CA time-series and PK parameters to
estimate the AIF itself.
[0060] Our experiments so far indicate great potential in our model
and validate it for population PK studies. It is of interest to
test this framework on larger data sets as well as on unseen data,
to study how effective the normalization is and how sensitive it is
to the choice of RR. It is also of interest to understand the
physical significance of our model parameters by studying their
relationships to the Tofts model parameters whose physical
significance is understood.
[0061] A method for implementing PK analysis in accordance with an
exemplary embodiment of the present invention will now be described
with reference to FIG. 5.
[0062] As shown in FIG. 5, time-series medical image data of a
patient who has been introduced with a contrast agent is received
(505). The medical image data is acquired during breast MRI, for
example. The time-series may pertain to an MR sequence that was
acquired at minute 0, an MR sequence that was acquired at minute 1,
which is a minute later than minute 0, an MR sequence that was
acquired at minute 2, which is a minute later than minute 1, etc.
It is to be understood that at least six or more time-points are
required for this implementation. However, if fewer than six
time-points are acquired, the number of time-points can be
increased by creating intermediary time-points by performing an
interpolation.
[0063] The time-series image data is input to a computer, such as a
server, for automated processing. During this processing, a
reference region (shown in FIG. 2B, for example) is identified
(510). A plurality of points of interest (shown in FIG. 2B, for
example) are also identified (515). A point of interest is a
potentially malignant tumor or mass in the patient's breast. It is
to be understood that the tumor candidates are detected by using a
computer-assisted detection technique such as one that detects
points where the increase in voxel intensity is above a certain
threshold, for example.
[0064] An intensity of voxels in the reference region is measured
(520). Here, we take the voxel intensity of the point detected by
the automatic nipple detector as taught by [Mert Dikmen, Yiqiang
Zhan, and Xing Sean Zhou. Joint Detection and Localization of
Multiple Anatomical Landmarks through Learning. SPIE Medical
Imaging, 2008]. For each point of interest, an intensity of voxels
therein is measured, as well (525).
[0065] The intensity measurements from steps 520 and 525 are used
to determine the density (c.sub.T(t)) of the contrast agent at the
point of interest and the density (c.sub.R(t)) of the contrast
agent at the reference region. Each density is determined by
approximating a difference in voxel intensities at different
time-points. The densities are input into equation (11) (530).
[0066] Equation (11) is solved to obtain five-parameter values
A.sub.1, B.sub.1, A.sub.2, B.sub.2, A.sub.3 (535). It is noted that
A.sub.1, B.sub.1, A.sub.2, B.sub.2, A.sub.3 are unknowns and the
values for these parameters are determined by performing a
numerical analysis such as Quadratic Discriminant Analysis. The
five-parameter values A.sub.1, B.sub.1, A.sub.2, B.sub.2, A.sub.3
are then used to select which of the points of interest are
malignant or not (540).
[0067] To automatically determine the set of values A.sub.1,
B.sub.1, A.sub.2, B.sub.2, A.sub.3 that indicate malignancy of the
point of interest, we prepared a training set where we calculated
A.sub.1, B.sub.1, A.sub.2, B.sub.2, A.sub.3 values at known
malignant points and at known benign points. Then we plotted
A.sub.1, B.sub.1, A.sub.2, B.sub.2, A.sub.3 in five-dimensional
space. Next, in this five-dimensional space, we calculated the
quadratic surface that best separates the values of A.sub.1,
B.sub.1, A.sub.2, B.sub.2, A.sub.3 of the known malignant points
from the known benign points. A point of interest is classified as
malignant if its plot in the five-dimensional space is on the
malignant side of the separation surface.
[0068] A system in which exemplary embodiments of the present
invention may be implemented will now be described with reference
to FIG. 6.
[0069] As shown in FIG. 6, the system includes a scanner 605, a
server 615 and a radiologist workstation 610 connected over a wired
or wireless network (indicated by the arrows). The scanner 605 may
be an MR scanner, for example.
[0070] The server 615 includes a central processing unit (CPU) 620,
a memory 625 and a PK analysis module 630 that includes program
code for executing methods in accordance with exemplary embodiments
of the present invention.
[0071] The radiologist workstation 610 includes a computer and
appropriate peripherals, such as a keyboard and display, and can be
operated in conjunction with the entire system. For example, the
radiologist workstation 610 may communicate with the scanner 605 so
that image data collected by the scanner 605 can be rendered at the
radiologist workstation 610 and viewed on the display. In addition,
the radiologist workstation 610 may communicate directly with the
server 615 to access previously processed image data, such as that
which has undergone our PK analysis, so that a radiologist can
manually verify the results of the PK analysis.
[0072] It is to be understood that the present invention may be
implemented in various forms of hardware, software, firmware,
special purpose processors, or a combination thereof. In one
embodiment, the present invention may be implemented in software as
an application program tangibly embodied on a program storage
device (e.g., magnetic floppy disk, RAM, CD ROM, DVD, ROM, and
flash memory). The application program may be uploaded to, and
executed by, a machine comprising any suitable architecture.
[0073] It should also be understood that because some of the
constituent system components and method steps depicted in the
accompanying figures may be implemented in software, the actual
connections between the system components (or the process steps)
may differ depending on the manner in which the present invention
is programmed. Given the teachings of the present invention
provided herein, one of ordinary skill in the art will be able to
contemplate these and similar implementations or configurations of
the present invention.
[0074] It is to be further understood that the above description is
only representative of illustrative embodiments. For convenience of
the reader, the above description has focused on a representative
sample of possible embodiments, a sample that is illustrative of
the principles of the invention. The description has not attempted
to exhaustively enumerate all possible variations. That alternative
embodiments may not have been presented for a specific portion of
the invention, or that further undescribed alternatives may be
available for a portion, is not to be considered a disclaimer of
those alternate embodiments. Other applications and embodiments can
be implemented without departing from the spirit and scope of the
present invention.
[0075] It is therefore intended, that the invention not be limited
to the specifically described embodiments, because numerous
permutations and combinations of the above and implementations
involving non-inventive substitutions for the above can be created,
but the invention is to be defined in accordance with the claims
that follow. It can be appreciated that many of those undescribed
embodiments are within the literal scope of the following claims,
and that others are equivalent.
* * * * *